 Semisimple representation

A representation is semisimple when it is a direct sum of irreducible representations. Equivalently, every invariant subspace has an invariant complement.

In mathematics, particularly in the field of representation theory, a semisimple representation refers to a specific type of representation of an algebraic structure such as a group, algebra, or Lie algebra. The concept is essential in understanding how these structures can act on vector spaces.